Finite hull systems and their implication bases. (Endliche Hüllensysteme und ihre Implikationenbasen.)
Whereas the Dedekind-MacNeille completion D(P) of a poset P is the minimal lattice L such that every element of L is a join of elements of P, the minimal strict completion D(P)∗ is the minimal lattice L such that the poset of join-irreducible elements of L is isomorphic to P. (These two completions are the same if every element of P is join-irreducible). In this paper we study lattices which are minimal strict completions of finite orders. Such lattices are in one-to-one correspondence with finite...
We show that the study of topological T0-spaces with a finite number of points agrees essentially with the study of polyhedra, by means of the geometric realization of finite spaces. In this paper all topological spaces are assumed to be T0.
A concrete category is (algebraically) universal if any category of algebras has a full embedding into , and is almost universal if there is a class of -objects such that all non-constant homomorphisms between them form a universal category. The main result of this paper fully characterizes the finitely generated varieties of -lattices which are almost universal.
In an -group with an appropriate operator set it is shown that the -value set can be embedded in the value set . This embedding is an isomorphism if and only if each convex -subgroup is an -subgroup. If has a.c.c. and is either representable or finitely valued, then the two value sets are identical. More generally, these results hold for two related operator sets and and the corresponding -value sets and . If is a unital -ring, then each unital -module over is an -module...
In this paper, we consider self-mappings defined on a metric space endowed with a finite number of graphs. Under certain conditions imposed on the graphs, we establish a new fixed point theorem for such mappings. The obtained result extends, generalizes and improves many existing contributions in the literature including standard fixed point theorems, fixed point theorems on a metric space endowed with a partial order and fixed point theorems for cyclic mappings.
The existence of fixed points for monotone maps on the fuzzy ordered sets under suitable conditions is proved.
Under suitable conditions we prove the existence of fixed points of fuzzy monotone multifunctions.